Fall 2021 and Spring 2022 Analysis Seminars: Difference between revisions

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'''Analysis Seminar
'''


The seminar will  meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.
The 2020-2021 Analysis Seminar will be organized by David Beltran and Andreas Seeger.
It will be online at least for the Fall semester, with details to be announced in September.
The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier to accomodate speakers).


If you wish to invite a speaker please contact Brian at street(at)math
Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230


===[[Previous Analysis seminars]]===
If you'd like to suggest  speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math).


= Analysis Seminar Schedule =
 
 
=[[Previous_Analysis_seminars]]=
 
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars
 
= Current Analysis Seminar Schedule =
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date   
!align="left" | date   
Line 16: Line 22:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|Sept 11
|September 22
| Simon Marshall
|Alexei Poltoratski
| UW Madison
|UW Madison
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]
|[[#Alexei Poltoratski |   Dirac inner functions ]]
|  
|  
|-
|-
|'''Wednesday, Sept 12'''
|September 29
| Gunther Uhlmann 
|Polona Durcik
| University of Washington
| Chapman University
| Distinguished Lecture Series
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
|  
|-
|-
|'''Friday, Sept 14'''
|September 30
| Gunther Uhlmann 
|Joris Roos
| University of Washington
|University of Massachusetts - Lowell
| Distinguished Lecture Series
|[[#linktoabstract  |  Title ]]
| See colloquium website for location
|  
|-
|-
|Sept 18
|October 6
| Grad Student Seminar
|Andrew Zimmer
|UW Madison
|[[#linktoabstract  |  Title ]]
|  
|  
|
|
|-
|-
|Sept 25
|October 13
| Grad Student Seminar
|Hong Wang
|
|Princeton/IAS
|
|[[#linktoabstract  |  Title ]]
|
|  
|-
|-
|Oct 9
|October 20
| Hong Wang
|Kevin Luli
| MIT
|UC Davis
|[[#Hong Wang About Falconer distance problem in the plane ]]
|[[#linktoabstract Title ]]
| Ruixiang
|  
|-
|-
|Oct 16
|October 27
| Polona Durcik
|Terence Harris
| Caltech
| Cornell University
|[[#Polona Durcik  |  Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]
|[[#linktoabstract Title ]]
| Joris
|-
|Oct 23
| Song-Ying Li
| UC Irvine
|[[#Song-Ying Li  |  Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]
| Xianghong
|-
|Oct 30
|Grad student seminar
|
|
|
|-
|Nov 6
| Hanlong Fang
| UW Madison
|[[#Hanlong Fang  |  A generalization of the theorem of Weil and Kodaira on prescribing residues ]]
| Brian
|-
||'''Monday, Nov. 12, B139'''
| Kyle Hambrook
| San Jose State University
|[[#Kyle Hambrook  |  Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]
| Andreas
|-
|Nov 13
| Laurent Stolovitch
| Université de Nice - Sophia Antipolis
|[[#Laurent Stolovitch Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]
|Xianghong
|-
|Nov 20
| Grad Student Seminar
|
|[[#linktoabstract  |    ]]
|  
|  
|-
|-
|Nov 27
|Monday, November 2, 4 p.m.
| No Seminar
|Yuval Wigderson
|  
|Stanford  University
|[[#linktoabstract  |   ]]
|[[#linktoabstract  |   Title ]]
|  
|  
|-
|-
|Dec 4
|November 10
| No Seminar
|Óscar Domínguez
|[[#linktoabstract  |   ]]
| Universidad Complutense de Madrid
|[[#linktoabstract  |   Title ]]
|  
|  
|-
|-
|Jan 22
|November 17
| Brian Cook
|Tamas Titkos
| Kent
|BBS U of Applied Sciences and Renyi Institute
|[[#Brian Cook Equidistribution results for integral points on affine homogenous algebraic varieties ]]
|[[#linktoabstract Title ]]
| Street
|-
|Jan 29
| No Seminar
|  
|  
|[[#linktoabstract  |    ]]
|
|-
|-
|Feb 5, '''B239'''
|November 24
| Alexei Poltoratski
|Shukun Wu
| Texas A&M
|University of Illinois (Urbana-Champaign)
|[[#Alexei Poltoratski  |  Completeness of exponentials: Beurling-Malliavin and type problems ]]
||[[#linktoabstract  |  Title ]]  
| Denisov
|-
|'''Friday, Feb 8'''
| Aaron Naber
| Northwestern University
|[[#linktoabstract  |  A structure theory for spaces with lower Ricci curvature bounds ]]
| See colloquium website for location
|-
|Feb 12
| Shaoming Guo
| UW Madison
|[[# Shaoming Guo | Polynomial Roth theorems in Salem sets  ]]
|  
|  
|-
|-
|'''Wed, Feb 13, B239'''
|December 1
| Dean Baskin
| Jonathan Hickman
| TAMU
| The University of Edinburgh
|[[# Dean Baskin  |  Radiation fields for wave  equations ]]
|[[#linktoabstract Title ]]
|  Colloquium
|-
|'''Friday, Feb 15'''
| Lillian Pierce
| Duke
|[[# Lillian Pierce  |  Short character sums ]]
|  Colloquium
|-
|'''Monday,  Feb 18, 3:30 p.m, B239.'''
| Daniel Tataru
| UC Berkeley
|[[#lDaniel Tataru  |  A Morawetz inequality for water waves ]]
|  PDE Seminar
|-
|Feb 19
| Wenjia Jing
|Tsinghua University
|Periodic  homogenization of Dirichlet problems in perforated domains: a unified proof
| PDE Seminar
|-
|Feb 26
| No Seminar
|
|
|-
|Mar 5
| Loredana Lanzani
| Syracuse University
|[[# Loredana Lanzani On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]
| Xianghong
|-
|Mar 12
| Trevor Leslie
| UW Madison
|[[# Trevor Leslie  |  Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]
|
|-
|Mar 19
|Spring Break!!!
|  
|  
|
|
|-
|-
|Mar 26
|December 8
| No seminar
|TBA
|  
|  
|[[#linktoabstract  |   ]]
|[[#linktoabstract  |   Title ]]
|  
|  
|-
|-
|Apr 2
|February 2
| Stefan Steinerberger
|Jongchon Kim
| Yale
| UBC
|[[#Stefan Steinerberger t  |  Wasserstein Distance as a Tool in Analysis ]]
| Shaoming, Andreas
|-
 
|Apr 9
| Franc Forstnerič
| Unversity of Ljubljana
|[[#linktoabstract  |  Title ]]
|[[#linktoabstract  |  Title ]]
| Xianghong, Andreas
|  
|-
|-
|Apr 16
|February 9
| Andrew Zimmer
|Bingyang Hu
| Louisiana State University
|Purdue University
|[[#linktoabstract  |  Title ]]
|[[#linktoabstract  |  Title ]]
| Xianghong
|  
|-
|-
|Apr 23
|February 16
| Person
|David Beltran
| Institution
|UW - Madison
|[[#linktoabstract  |  Title ]]
|[[#linktoabstract  |  Title ]]
| Sponsor
|-
|Apr 30
| Reserved
| Institution
|[[#linktoabstract  |  Title ]]
| Shaoming
|-
|}
|}


=Abstracts=
=Abstracts=
===Simon Marshall===
''Integrals of eigenfunctions on hyperbolic manifolds''
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X.  I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity.  I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.
===Hong Wang===
''About Falconer distance problem in the plane''
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou.
===Polona Durcik===
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.
===Song-Ying Li===
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the
Kohn Laplacian on strictly pseudoconvex hypersurfaces.
===Hanlong Fan===
''A generalization of the theorem of Weil and Kodaira on prescribing residues''
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.
===Kyle Hambrook===
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''
I will discuss my recent work on some problems concerning
Fourier decay and Fourier restriction for fractal measures on curves.
===Laurent Stolovitch===
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$  are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.
===Brian Cook===
''Equidistribution results for integral points on affine homogenous algebraic varieties''
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.
===Alexei Poltoratski===
===Alexei Poltoratski===


''Completeness of exponentials: Beurling-Malliavin and type problems''
Title: Dirac inner functions


This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.
Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations.
We will discuss connections between problems in complex function theory, spectral and scattering problems for differential
operators and the non-linear Fourier transform.




===Shaoming Guo===
===Name===


''Polynomial Roth theorems in Salem sets''
Title


Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik.
Abstract




===Name===


Title


===Dean Baskin===
Abstract


''Radiation fields for wave equations''


Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
===Name===


===Lillian Pierce===
Title


''Short character sums''
Abstract


A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.


===Loredana Lanzani===
===Name===


''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''
Title


This talk is a survey of my latest, and now final, collaboration with Eli Stein.
Abstract


It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.)  We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.
=Extras=
 
[[Blank Analysis Seminar Template]]
===Trevor Leslie===
 
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''


In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity.  Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1.  In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time.  When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution.  The work described is joint with Roman Shvydkoy (UIC).


+++Stefan Steinerberger===
Graduate Student Seminar:


''Wasserstein Distance as a Tool in Analysis''
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html
 
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.
 
=Extras=
[[Blank Analysis Seminar Template]]

Revision as of 00:30, 20 September 2020

The 2020-2021 Analysis Seminar will be organized by David Beltran and Andreas Seeger. It will be online at least for the Fall semester, with details to be announced in September. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar earlier to accomodate speakers).

Zoom links will be sent to those who have signed up for the Analysis Seminar List. For instructions how to sign up for seminar lists, see https://www.math.wisc.edu/node/230

If you'd like to suggest speakers for the spring semester please contact David and Andreas (dbeltran at math, seeger at math).


Previous_Analysis_seminars

https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars

Current Analysis Seminar Schedule

date speaker institution title host(s)
September 22 Alexei Poltoratski UW Madison Dirac inner functions
September 29 Polona Durcik Chapman University Title
September 30 Joris Roos University of Massachusetts - Lowell Title
October 6 Andrew Zimmer UW Madison Title
October 13 Hong Wang Princeton/IAS Title
October 20 Kevin Luli UC Davis Title
October 27 Terence Harris Cornell University Title
Monday, November 2, 4 p.m. Yuval Wigderson Stanford University Title
November 10 Óscar Domínguez Universidad Complutense de Madrid Title
November 17 Tamas Titkos BBS U of Applied Sciences and Renyi Institute Title
November 24 Shukun Wu University of Illinois (Urbana-Champaign) Title
December 1 Jonathan Hickman The University of Edinburgh Title
December 8 TBA Title
February 2 Jongchon Kim UBC Title
February 9 Bingyang Hu Purdue University Title
February 16 David Beltran UW - Madison Title

Abstracts

Alexei Poltoratski

Title: Dirac inner functions

Abstract: My talk will focus on some new (and old) complex analytic objects arising from Dirac systems of differential equations. We will discuss connections between problems in complex function theory, spectral and scattering problems for differential operators and the non-linear Fourier transform.


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract


Name

Title

Abstract

Extras

Blank Analysis Seminar Template


Graduate Student Seminar:

https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html